I make my living doing electrical work but bear in mind that opinions vary form one electrician to another and code varies from location to location... With that said I would be surprised if you need to upgrade the 125 for your intended use. If you do start tripping the 125 eliminate the possibility of a weak breaker BEFORE you consider upgrading.
As for your wire runs they may or may not be compliant, depending on your local. Way back when copper was cheap we squared our corners and ran things neatly. These days we mostly run as little wire as possible, running straight from point A to point B which can leave quite a tangle. Doing neat work has given way to keeping the cost down. You are correct in that it is an eyesore as well as sometimes an inconvenience, but in today's cutthroat construction economy...
You shouldn't have a problem bundling wires if they are all carrying line voltage. It can create problems if you include low voltage, phone, or data cables in your bundle. You can build an electrical chase with 3 boards placed like this |_| and re-run your wiring inside for a neat, well protected attic space.
Hope that helps.